Lesson video

Hello there, my name is Mr. Goldy, and welcome to today's maths lesson.

I'm sure you're going to have lots of fun.

And here is our lesson outcome.

I can bridge 100 by adding or subtracting a single digit number.

And here are the key words for today's lesson, so the key words are bridge or bridging.

Can you say bridge? Can you say bridging? Excellent.

And the other key word is partition.

Can you say partition? Let's look at what those words mean.

So bridging is a strategy which uses addition or subtraction to cross a number boundary.

You can bridge 100 by adding to make 100 and then adding whatever is left.

For example, you can add 97 add six by bridging.

97 add three equals 100.

And then, 100 add three equals 103.

Partition means splitting a number into parts.

Six can be partitioned into three and three or four and two.

And here's our lesson outline.

The first part of today's lesson is going to be bridging 100 using pictorial representations, and the second part will be bridging 100 using number line representations.

Let's get started.

In this lesson, you will meet Jacob and Aisha.

You can represent numbers using base 10 blocks.

100 looks like this, 10 looks like this, and one looks like this.

And you can represent 107 like this.

So we've got there 100 and seven ones, 107.

Numbers below 100 can also be represented using an empty 100 square.

So this can look just like a base ten 100 block.

So 99 would look like this.

So 100 squares altogether, 99 of them are blue.

91 looks like this.

There are 100 squares altogether, 91 of them are blue.

94 would look like this, so 94 blue squares altogether.

Use number pairs that total 10 to make 100.

What do you add to equal 100? 99 add one equals 100, nine add one equals 10, 99 add one equals 100.

91 add nine equals 100.

One add nine equals 10.

91 add nine equals 100.

94 add six equals 100.

Four add six equals 10.

94 add six equals 100.

Okay, maths is full of patterns, and it's all about spotting those patterns.

Jacob calculates eight add four.

There's a 10 block with eight of them coloured blue and two are white.

And we've got four ones.

Jacob partitions four into two and two, then he adds two to make 10.

So two add eight equals 10, then he adds two to make 12.

So eight add four equals 12.

Aisha calculates 98 add four.

Aisha partitions four into two and two, then she adds two to make 100.

So she's partitioned that four into two and two, and she's going to add two to the 98 to make 100.

Then she adds two to make 102.

98 add four equals 102.

So eight add four equals 12, 98 add four equals 102.

Jacob calculates eight add six.

Jacob first partitions six into two and four.

So eight add two, of course, makes 10, then he adds two to make 10.

So he's left with 10 and four ones.

10 and four ones equals 14.

Eight add six equals 14.

Aisha calculates 98 add six, so she's using the same number facts to help her get to the answer.

Aisha partitions six into two and four, then she adds two to make 100.

Eight add two equals 10.

98 add two equals 100, and she's left with 100 and four ones.

98 add six equals 104.

Aisha calculates 97 add seven.

How should I partition seven to bridge 100? What number added to 97 equals 100? What do you think Aisha's gonna have to add first? Aisha partitions seven into three and four.

Seven add three equals 10.

97 add three equals 100, then she adds three to make 100.

She's left with 100 and four ones.

100 and four ones equals 104.

97 add seven equals 104.

Aisha calculates 94 add seven.

How should I partition seven to bridge 100? What number added to 94 equals 100? And don't forget, use those number pairs that total 10.

Four add what number equals 10? 94 add what number equals 100? Aisha partitions seven into six and one, then she adds six to make 100.

She's left with 100 and one.

94 add seven equals 101.

Here's one to try on your own.

Aisha calculates 95 add seven.

How should I partition seven to bridge 100? Jacob's given you a bit of a clue here.

What number added to 95 equals 100? Pause the video.

How would you add together 95 and seven? And welcome back, how did you get on? Did you get the answer? Did you partition seven in the right way, the most efficient way? Let's have a look.

So Aisha partitions seven into five and two.

Five add five equals 10.

95 add five equals 100.

Aisha partitions the seven into five and two, then she adds five to make 100.

And she's left with 100 and two.

95 add seven equals 102.

Jacob calculates 13 subtract five.

He partitions five into three and two.

He subtracts three to make 10, then he subtracts two.

Remember, he's gotta subtract five altogether.

He subtracted three already, he's now gonna subtract two.

13 subtract five equals eight.

Aisha calculates 103 subtract five.

There's 100 and three ones.

She partitions five into three and two, so she's subtracting five, she's gonna break it up into three and two.

She subtracts three to make 100, then she subtracts two.

What is she left with? 103 subtract five equals 98.

So it's the same number facts that Aisha used to help her calculate 103 subtract five.

Aisha calculates 105 subtract seven.

"What should I subtract first?", says Aisha.

So first, she subtracts five to make 100.

Let's take away those five ones.

We're left with 100.

What does Aisha still have to subtract? What does she still have to take away from 100? She had to subtract seven altogether.

She subtracted five, how many more does she still have to subtract? So next, Aisha subtracts two.

So 105 subtract seven equals 98.

Now here's one to try on your own.

Aisha calculates 102 subtract seven.

"What should I subtract first?", says Aisha.

What should Aisha subtract next? How should Aisha calculate the answer to 102 subtract seven? How is she going to partition the seven to subtract it from 102? Pause the video, have a think about it, and see if you can work out the answer.

Welcome back.

Did you manage to partition seven in an efficient way? Did you manage to get the answer? Let's have a look to see if you were right.

So first of all, Aisha subtracts two to make 100, then she subtracts five.

Remember, she had to subtract seven altogether.

She subtracted two already, she still has to subtract five.

100 subtract five equals 95.

102 subtract seven equals 95.

Very well done, if you got the right answer.

What is the missing addend? 98 add something equals 105.

What do you have to add to a 98 to get to 105? First, add two to equal 100.

Let's add two on first of all, gets us to 100.

What do you still have to add to get to 105? Then add five to equal 105.

What has been added altogether? We've added two, we've added five.

Five add two equals seven.

98 add seven equals 105.

Now here's one to try on your own.

What is the missing addend? 98 add what number equals 107? Pause the video.

Can you work out the answer? Welcome back.

Did you manage to get the answer? Let's have a look if you were right.

So first of all, what did you have to add to 98 to get to 100? First, add two to equal 100, then add seven to equal 107.

What has been added altogether? What did you add altogether? You added two, then you added seven, altogether you added nine.

98 add nine equals 107.

Very well done, if you got the right answer.

And let's move on to our task.

So the first part of the task, you've got to find numbers to make these calculations correct.

So you've got some representations there to help you, and you've got to work out either the sum of the two addends or work out the missing addend.

But use those representations to help you work out the answer.

Part two, find numbers to make these calculations correct.

So this time you've gotta work out the differences or work out the missing subtrahends.

So what do you have to take away to get the difference? So pause the video and have a go at task A.

Welcome back.

Let's see how you got on.

So here are our answers for part one.

So our missing sums and our missing addends, here are the answers you should have got.

So you can pause the video, if you want to have a look at those.

And here's part two.

So 103 subtract four equals 99.

103 subtract eight equals 95.

Well done, if you managed to have a go at both parts of task A and you managed to get lots and lots of practise in.

That's really important.

And let's move on to the second part of the lesson.

So the second part of the lesson is bridging 100 using number line representations.

Aisha completes a calculation.

What number equals 98 add five? "I'm going to use a number line to find the sum," says Aisha.

So, here's a number line.

It starts at 90, goes all the way to 110.

First, Aisha partitions five into two and three.

So remember, it's using number pairs to 10 to help you bridge 100.

Eight add two equals 10.

98 add two equals 100.

Then she adds two.

She starts from 98, adds two, that gets us to 100.

Then she adds three, so she adds three more, so now she's added five altogether.

Two add three equals five.

103 equals 98 add five.

Aisha completes a calculation.

This time she's calculating 105 subtract seven.

"I'm going to use a number line to find the difference," says Aisha.

At first, Aisha partitions seven into five and two, so she wants to count back to 100.

She starts from 105, and she has to subtract five to get back to 100.

Then she subtracts five.

If she subtracts five from 105, she gets the answer 100, then she subtracts two more.

Remember, she's got to subtract seven altogether.

If she subtracts five and then two more, she's subtracted seven altogether.

So subtract another two would equal 98.

105 subtract seven equals 98.

Complete the calculation, 102 subtract eight.

How would you use a number line to find the difference? How would you use a number line to find the difference? Pause the video and see if you can work out the answer.

Did you manage to get the answer? Did you manage to partition eight efficiently? Let's have a look to see how you did it.

So first, partition eight into two and six.

So starting from 102, you want to subtract two first of all, and then you have to subtract another six, so you subtracted eight altogether.

Then subtract two.

Let's start from 102 and subtract two, that gets us to 100, so we are bridging that 100.

Then subtract six, and this is where your number pairs to 10 are still very, very helpful.

10 subtract six equals four.

So then 100 subtract six equals 94.

So the answer is 94.

102 subtract eight equals 94.

Aisha completes a calculation, 105 equals 98 add what number? What's the missing addend? "I'm going to use a number line to find the missing addend," says Aisha.

So Aisha would start at 98 and she'd add on two to get to 100 to equal 100.

So 98 add two equals 100.

Remember, it's all about bridging 100.

Then she adds five to equal 105, 'cause she wants to see what number you have to add to 98 to equal 105.

Add five on, we get to 105.

105 equals 98 add seven.

Aisha completes a calculation, it's another missing number problem.

103 subtract what number equals 97? "I'm going to use a number line to find the missing number," says Aisha.

First, Aisha subtracts back to 100, so she's going to start from 103, and she's going to subtract back to get to 100.

103 subtract three equals 100, then she subtracts back to 97.

So what would she have to subtract from 100 to get to 97? And again, use your number pairs to 10.

10 subtract three equals seven, so 100 subtract three must equal 97.

So we subtract three again, we get our answer, 97.

What's been subtracted altogether? Three's been subtracted, then another three was subtracted.

Altogether, six has been subtracted.

103 subtract six equals 97.

Here's one to have a go at your own.

Complete the calculation, 102 subtract what number equals 95? Pause the video and see if you can work out the answer.

And welcome back.

Did you get the right answer? Let's find out if you were right.

First, subtract back to 100.

You should have started on 102 and subtracted two to get to 100.

102 subtract two equals 100.

So then you have to subtract back to 95.

100 subtract five equals 95.

If 10 subtract five is five, 100 subtract five equals 95.

What's been subtracted altogether? Seven, 102 subtract seven equals 95.

Very well done, if you got seven as the missing number.

Jacob has these number cards.

So he's got the number cards zero all the way to nine.

He uses some of them to make this equation correct.

So 90 something add seven equals 100 and something.

The zero, the one, the seven, and the nine have already been used, so let's cross those out to show they've already been used.

So he used the zero and the one and the seven and the nine.

So maybe he could use the eight, maybe he could start with 98.

98 add two equals 100.

Two add five equals seven.

So he adds another five on, he gets the answer 105.

So the missing numbers could be 98 and 105.

98 add seven equals 105.

And here's one to try on your own.

So Jacob has these number cards.

Remember, he's already used the zero, the one, seven, and the nine.

How else could he complete the equation? Pause the video and see if you can use two other number cards to make that equation correct.

And welcome back.

How did you get on? Did you manage to find another possible solution? Let's have a look.

So here is another possible answer.

So Jacob could have started on 95 and added five to get to 100 and then added two to get to 102.

Remember, you have to add seven.

The missing number cards could be 95 and 102.

95 add seven equals 102.

Aisha has these number cards, so same number cards.

She uses some of them to make this equation correct.

So 100 and something subtract something equals 98, because there are two missing number cards.

The zero, the one, the eight, and the nine have already been used, let's cross those out.

So the zero's been used, the one's been used, the eight's been used, and nine's been used already in the equation.

So first of all, Aisha subtracts four to get to 104, then she subtracts two more to get to 98.

So Aisha thinks the starting number could be 104.

What number has she subtracted altogether? Well, she subtracted four and she subtracted two, she subtracted six altogether.

So the missing numbers could be 104 subtract six equals 98.

Aisha has these number cards.

How else could she complete the equation? She's gonna use a number line to help work out the answer.

She's already done 104 subtract six, is there another way of completing that equation using those remaining number cards? Pause the video and see if you can find an answer.

And welcome back.

Did you manage to find a solution? Let's see how you got on.

Here is another possible answer.

105 subtract five equals 100 and then subtract two more, that gets us to the number 98.

What's been subtracted altogether? Subtract five and subtract two, seven has been subtracted altogether.

So missing numbers could be 105 subtract seven, that would also equal 98.

And there are other possible answers too.

So well done, if you managed to come up with a solution to that problem.

Let's move on to task B.

The first part of task B is use the number cards zero to nine to make these equations correct.

A card can only be used once in each equation and if it's already been used, you can't use it again.

So that first one, 104 subtract something equals 90 something, the numbers one and zero and four and nine have already been used, you can't use them again.

Use number lines to help you represent each problem.

Can you find more than one answer? There's two different equations there.

Can you find more than one answer to each equation? And then part two, use the number cards zero to nine to make these equations correct.

A card can only be used once in each equation, and again, can you find more than one answer? So pause the video, have a good think.

You might actually want to get some number cards and use 'em to help you.

Can you find different solutions to those problems? And welcome back.

So for the first part, here are the answers.

You may have come up with the calculations, 104 subtract six equals 98, or you may have come up with 104 subtract eight equals 96, or you may have come up with both of them.

Very well done, if you did.

And 97 add five equals 102.

97 add six equals 103.

And 97 add eight equals 105.

Well done, if you found all possible answers for that problem.

And for part two, here are all the different possible answers.

So 102 subtract seven equals 95.

103 subtract seven equals 96.

105 subtract seven equals 98.

And the other problem, there were four different possible answers.

Very well done, if you managed to find all four possible answers.

So well done for working hard in today's lesson, and I hope you're feeling much more confident at adding and subtracting across the 100's boundary.

Excellent work today, well done.

And here is our lesson summary.

So when adding, start with the largest number and partition the smaller number.

Count on to 100, then add on the remainder.

When subtracting, count back to 100 and then subtract the remainder.

Use number pairs that total 10 to help you bridge 100.